Regular partitions of dual polar spaces

We describe several classes of regular partitions of dual polar spaces and determine their associated parameters and eigenvalues. We also give some general methods for computing the eigenvalues of regular partitions of dual polar spaces.     

Asymptotic formulae for multivariate Kantorovich type generalized sampling series

In this paper an asymptotic formula of Voronovskaja type for a multivariate extension of the Kantorovich generalized sampling series is given. Moreover a quantitative version in terms of some moduli of smoothness is established. Finally some particular examples of kernels are discussed, as the Bochner-Riesz kernel and the multivariate splines.     

Invariant regions for the Nernst-Planck equations

We consider a coupling between the Nernst-Planck equations and the Navier-Stokes system; we study the stationary and the evolution problems. The crucial property turns out to be the existence of an invariant region. An asymptotic result in the case of Neumann boundary conditions is also given.     

A Sharp Upper Bound for the¶Torsional Rigidity of Rods¶by Means of Web Functions

Using web functions, we approximate the Dirichlet integral which represents the torsional rigidity of a cylindrical rod with planar convex cross-section Ω. To this end, we use a suitably defined piercing function, which enables us to obtain bounds for both the approximate and the exact value of the torsional rigidity. When Ω varies, we show that the ratio between these two values is always larger than ¾; we prove that this is a sharp lower bound and that it is not attained. Several extremal cases are also analyzed and studied by numerical methods.     

Bergamot (<Emphasis Type="Italic">Citrus bergamia</Emphasis> Risso) fruit extracts and identified components alter expression of interleukin 8 gene in cystic fibrosis bronchial epithelial cell lines

Background  

Cystic fibrosis (CF) airway pathology is a fatal, autosomal, recessive genetic disease characterized by extensive lung inflammation. After induction by TNF-α, elevated concentrations of several pro-inflammatory cytokines (i.e. IL-6, IL-1β) and chemokines (i.e. IL-8) are released from airway epithelial cells. In order to reduce the excessive inflammatory response in the airways of CF patients, new therapies have been developed and in this respect, medicinal plant extracts have been studied. In this article we have investigated the possible use of bergamot extracts (Citrus bergamia Risso) and their identified components to alter the expression of IL-8 associated with the cystic fibrosis airway pathology.     

Design,Synthesis and Evaluation of New Multifunctional Benzothiazoles as Photoprotective,Antioxidant and Antiproliferative Agents

A current trend of research in the health field is toward the discovery of multifunctional compounds, capable of interacting with multiple biological targets, thus simplifying multidrug therapies and improving patient compliance. The aim of this work was to synthesize new multifunctional chemical entities bearing a benzothiazole nucleus, a structure that has attracted increasing interest for the great variety of biological actions that it can perform, and already used as a scaffold in several multifunctional drugs. Compounds are reported, divided into two distinct series, synthetized and tested in vitro for the antioxidant, and include UV-filtering and antitumor activities. DPPH and FRAP tests were chosen to outline an antioxidant activity profile against different radical species. The UV-filtering activity was investigated, pre- and post-irradiation, through evaluation of a O/W sunscreen standard formulation containing 3% of the synthetic compounds. The antitumor activity was investigated both on human melanoma cells (Colo-38) and on immortalized human keratinocytes as a control (HaCat). A good antiproliferative profile in terms of IC₅₀ was chosen as a mandatory condition to further investigate apoptosis induction as a possible cytotoxicity mechanism through the Annexin V test. Compound BZTcin4 was endowed with excellent activity and a selectivity profile towards Colo-38, supported by a good antioxidant capacity and an excellent broad-spectrum photoprotective profile.     

Synergistic Effect of Bioactive Monoterpenes against the Mosquito,Culex pipiens (Diptera: Culicidae)

Mosquitoes represent one of the most important vectors and are responsible for the transmission of many arboviruses that affect human and animal health. The chemical method using synthetic insecticides disturbs the environmental system and promotes the appearance of resistant insect species. Therefore, this study investigated the insecticidal effect of some binary monoterpene combinations (1,8 cineole + α-pinene and carvone + R (+)-pulegone) using a mixture design approach. The fumigant toxicity was evaluated against Culex pipiens female adults using glass jars. The results show that the toxicity varies according to the proportions of each compound. Indeed, Mixture 1 (1,8-cineole + α-pinene) displayed a strong toxic effect (51.00 ± 0.86% after 24 h and 100.00 ± 0.70% after 48 h) when the pure compounds were tested at 0.25/0.75 proportions of 1,8-cineole and α-pinene, respectively. Nevertheless, the equal proportion (0.5/0.5) of carvone and R (+)-pulegone in Mixture 2 exhibited a toxic effect of 54.35 ± 0.75% after 24 h and 89.96 ± 0.14% after 48 h, respectively. For Mixture 1, the maximum area of mortality that the proposed model indicated was obtained between 0/1 and 0.25/0.75, while the maximum area of mortality in the case of Mixture 2 was obtained between 0.25/0.75 and 0.75/0.25. Moreover, the maximum possible values of mortality that could be achieved by the validated model were found to be 51.44% (after 24 h) and 100.24% (after 48 h) for Mixture 1 and 54.67% (after 24 h) and 89.99% (after 48 h) for Mixture 2. It can be said that all purev molecules tested through the binary mixtures acted together, which enhanced the insecticide’s effectiveness. These findings are very promising, as the chemical insecticide (deltamethrin) killed only 19.29 ± 0.01% and 34.05 ± 1.01% of the female adults after 24 h and 48 h, respectively. Thus, the findings of our research could help with the development of botanical insecticides that might contribute to management programs for controlling vectors of important diseases.     

Overdetermined problems with possibly degenerate ellipticity, a geometric approach

Given an open bounded connected subset Ω of ℝⁿ, we consider the overdetermined boundary value problem obtained by adding both zero Dirichlet and constant Neumann boundary data to the elliptic equation −div(A(|∇u|)∇u)=1 in Ω. We prove that, if this problem admits a solution in a suitable weak sense, then Ω is a ball. This is obtained under fairly general assumptions on Ω and A. In particular, A may be degenerate and no growth condition is required. Our method of proof is quite simple. It relies on a maximum principle for a suitable P-function, combined with some geometric arguments involving the mean curvature of ∂Ω.